Green Card

Alex, thank you for your question. With respect to the portion of your question that asks can your father who is a lawful permanent resident apply for an immigrant visa for you, the short answer is yes. You would qualify as a 2B preference and the proper form for this petition is the I-130. Unfortunately there is a substantial waiting period for visa applications for people in your category. The current waiting period is about 9 years.

The DV lottery is free but there are several websites out there that charge to file and application and try to appear to be the official site. The State Department website has a good discussion of the program:

http://travel.state.gov/visa/immigrants/types/types_1322.html

and the official site for the DV program is here but the program is closed for this year:

http://www.dvlottery.state.gov/